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I am doing the revision, and confusing about the face amount, net single premium and annual net premium. As I know the net single premium is the present value of the lump sum pay at time 0. How about the annual net premium and face amount?

For a fully continuous 20-year term life insurance on () with face amount 1,000, you are given:

  • The net single premium is 150.
  • The annual net premium is 15.15.
  • =0.06.

Determine 20px

Jessica J
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Apr 19 '22 at 04:22

1 Answers1

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"Face amount" is the benefit; i.e., the amount the policy pays out in case the insured dies within the policy term.

"Net single premium" is the actuarial present value of the policy at the time of issue; i.e., the up front price of the policy at the time of issue that the insurer has calculated that equals the expected present value of the benefit, accounting for the future lifetime random variable of the insured.

"Annual net premium" is the amount of premium paid by the policyholder if payments are made annually at the beginning of each policy year until the insured dies or the term ends, whichever occurs sooner.

Now that these terms have been defined, you should make an attempt at solving the problem, and share your work with us.

heropup
  • 135,869
  • So does it mean by reffering this question the Actuarial Present Value Benefit = 150=1000E(Z)? – Jessica J Apr 19 '22 at 05:32
  • @JessicaJ Yes, if by $Z$ you mean $$Z = \begin{cases}v^T, & 0 \le T \le 20, \ 0, & T > 20 \end{cases}$$ where $T$ is the future lifetime random variable of the insured at the moment of policy issue. In actuarial notation, $$\require{enclose} 150 = 1000 \overline{A}_{x : \enclose{actuarial}{20}}^1.$$ – heropup Apr 19 '22 at 06:14